Xử lý hình ảnh kỹ thuật số P16

Xử lý hình ảnh kỹ thuật số P16

IMAGE FEATURE EXTRACTION
An image feature is a distinguishing primitive characteristic or attribute of an image. Some features are natural in the sense that such features are defined by the visual appearance of an image, while other, artificial features result from specific manipulations of an image. Natural features include the luminance of a region of pixels and gray scale textural regions. Image amplitude histograms and spatial frequency spectra are examples of artificial features.

514 IMAGE FEATURE EXTRACTION
m,n
r q
j,k
FIGURE 16.2-2. Relationship of pixel pairs.
The factor of 3 inserted in the expression for the Kurtosis measure normalizes SK to
zero for a zero-mean, Gaussian-shaped histogram. Another useful histogram shape
measure is the histogram mode, which is the pixel amplitude corresponding to the
histogram peak (i.e., the most commonly occurring pixel amplitude in the window).
If the histogram peak is not unique, the pixel at the peak closest to the mean is usu-
ally chosen as the histogram shape descriptor.
Second-order histogram features are based on the definition of the joint proba-
bility distribution of pairs of pixels. Consider two pixels F ( j, k ) and F ( m, n ) that
are located at coordinates ( j, k ) and ( m, n ), respectively, and, as shown in Figure
16.2-2, are separated by r radial units at an angle θ with respect to the horizontal
axis. The joint distribution of image amplitude values is then expressed as
P ( a, b ) = P R [ F ( j, k ) = r a, F ( m, n ) = r b ] (16.2-11)
where r a and r b represent quantized pixel amplitude values. As a result of the dis-
crete rectilinear representation of an image, the separation parameters ( r, θ ) may
assume only certain discrete values. The histogram estimate of the second-order dis-
tribution is
N ( a, b )
P ( a, b ) ≈ -----------------
- (16.2-12)
M
where M is the total number of pixels in the measurement window and N ( a, b )
denotes the number of occurrences for which F ( j, k ) = r a and F ( m, n ) = r b .
If the pixel pairs within an image are highly correlated, the entries in P ( a, b ) will
be clustered along the diagonal of the array. Various measures, listed below, have
been proposed (6,7) as measures that specify the energy spread about the diagonal of
P ( a, b ).
Autocorrelation:
L–1 L–1
SA = ∑ ∑ abP ( a, b ) (16.2-13)
a=0 b=0

516 IMAGE FEATURE EXTRACTION
16.3. TRANSFORM COEFFICIENT FEATURES
The coefficients of a two-dimensional transform of a luminance image specify the
amplitude of the luminance patterns (two-dimensional basis functions) of a trans-
form such that the weighted sum of the luminance patterns is identical to the image.
By this characterization of a transform, the coefficients may be considered to indi-
cate the degree of correspondence of a particular luminance pattern with an image
field. If a basis pattern is of the same spatial form as a feature to be detected within
the image, image detection can be performed simply by monitoring the value of the
transform coefficient. The problem, in practice, is that objects to be detected within
an image are often of complex shape and luminance distribution, and hence do not
correspond closely to the more primitive luminance patterns of most image trans-
forms.
Lendaris and Stanley (8) have investigated the application of the continuous two-
dimensional Fourier transform of an image, obtained by a coherent optical proces-
sor, as a means of image feature extraction. The optical system produces an electric
field radiation pattern proportional to
∞ ∞
F ( ω x, ω y ) = ∫–∞ ∫–∞ F ( x, y ) exp { – i ( ωx x + ωy y ) } dx dy (16.3-1)
where ( ω x, ω y ) are the image spatial frequencies. An optical sensor produces an out-
put
2
M ( ω x, ω y ) = F ( ω x, ω y ) (16.3-2)
proportional to the intensity of the radiation pattern. It should be observed that
F ( ω x, ω y ) and F ( x, y ) are unique transform pairs, but M ( ω x, ω y ) is not uniquely
related to F ( x, y ) . For example, M ( ω x, ω y ) does not change if the origin of F ( x, y )
is shifted. In some applications, the translation invariance of M ( ω x, ω y ) may be a
benefit. Angular integration of M ( ω x, ω y ) over the spatial frequency plane produces
a spatial frequency feature that is invariant to translation and rotation. Representing
M ( ω x, ω y ) in polar form, this feature is defined as
2π
N (ρ) = ∫0 M ( ρ, θ ) dθ (16.3-3)
2 2 2
where θ = arc tan { ω x ⁄ ω y } and ρ = ω x + ω y . Invariance to changes in scale is an
attribute of the feature
∞
P(θ ) = ∫0 M ( ρ, θ ) dρ (16.3-4)

TEXTURE DEFINITION 519
for u, v = 0, …, N – 1 can be examined directly for feature extraction purposes. Hor-
izontal slit, vertical slit, ring, and sector features can be defined analogous to
Eqs. 16.3-5 to 16.3-8. This concept can be extended to other unitary transforms,
such as the Hadamard and Haar transforms. Figure 16.3-2 presents discrete Fourier
transform log magnitude displays of several geometric shapes.
16.4. TEXTURE DEFINITION
Many portions of images of natural scenes are devoid of sharp edges over large
areas. In these areas, the scene can often be characterized as exhibiting a consistent
structure analogous to the texture of cloth. Image texture measurements can be used
to segment an image and classify its segments.
Several authors have attempted qualitatively to define texture. Pickett (9) states
that “texture is used to describe two dimensional arrays of variations... The ele-
ments and rules of spacing or arrangement may be arbitrarily manipulated, provided
a characteristic repetitiveness remains.” Hawkins (10) has provided a more detailed
description of texture: “The notion of texture appears to depend upon three ingredi-
ents: (1) some local 'order' is repeated over a region which is large in comparison to
the order's size, (2) the order consists in the nonrandom arrangement of elementary
parts and (3) the parts are roughly uniform entities having approximately the same
dimensions everywhere within the textured region.” Although these descriptions of
texture seem perceptually reasonably, they do not immediately lead to simple quan-
titative textural measures in the sense that the description of an edge discontinuity
leads to a quantitative description of an edge in terms of its location, slope angle,
and height.
Texture is often qualitatively described by its coarseness in the sense that a patch
of wool cloth is coarser than a patch of silk cloth under the same viewing conditions.
The coarseness index is related to the spatial repetition period of the local structure.
A large period implies a coarse texture; a small period implies a fine texture. This
perceptual coarseness index is clearly not sufficient as a quantitative texture mea-
sure, but can at least be used as a guide for the slope of texture measures; that is,
small numerical texture measures should imply fine texture, and large numerical
measures should indicate coarse texture. It should be recognized that texture is a
neighborhood property of an image point. Therefore, texture measures are inher-
ently dependent on the size of the observation neighborhood. Because texture is a
spatial property, measurements should be restricted to regions of relative uniformity.
Hence it is necessary to establish the boundary of a uniform textural region by some
form of image segmentation before attempting texture measurements.
Texture may be classified as being artificial or natural. Artificial textures consist of
arrangements of symbols, such as line segments, dots, and stars placed against a
neutral background. Several examples of artificial texture are presented in Figure
16.4-1 (9). As the name implies, natural textures are images of natural scenes con-
taining semirepetitive arrangements of pixels. Examples include photographs
of brick walls, terrazzo tile, sand, and grass. Brodatz (11) has published an album of
photographs of naturally occurring textures. Figure 16.4-2 shows several natural
texture examples obtained by digitizing photographs from the Brodatz album.

520 IMAGE FEATURE EXTRACTION
FIGURE 16.4-1. Artificial texture.

VISUAL TEXTURE DISCRIMINATION 521
(a) Sand (b) Grass
(c) Wool (d) Raffia
FIGURE 16.4-2. Brodatz texture fields.
16.5. VISUAL TEXTURE DISCRIMINATION
A discrete stochastic field is an array of numbers that are randomly distributed in
amplitude and governed by some joint probability density (12). When converted to
light intensities, such fields can be made to approximate natural textures surpris-
ingly well by control of the generating probability density. This technique is useful
for generating realistic appearing artificial scenes for applications such as airplane
flight simulators. Stochastic texture fields are also an extremely useful tool for
investigating human perception of texture as a guide to the development of texture
feature extraction methods.
In the early 1960s, Julesz (13) attempted to determine the parameters of stochas-
tic texture fields of perceptual importance. This study was extended later by Julesz
et al. (14–16). Further extensions of Julesz’s work have been made by Pollack (17),

526 IMAGE FEATURE EXTRACTION
(a) Constrained second-order density
(b) Constrained third-order density
FIGURE 16.5-4. Row correlation factors for stochastic field generation. Dashed line, field
A; solid line, field B.
1 α β γ …
α
KJ + 1 = –2 (16.5-7)
β σ KJ
γ
…
where α, β, γ, … denote correlation lag terms. Figure 16.5-4 presents an example of
the row correlation functions used in the texture field comparison tests described
below.
Figures 16.5-5 and 16.5-6 contain examples of Gaussian texture field comparison
tests. In Figure 16.5-5, the first-order densities are set equal, but the second-order
nearest neighbor conditional densities differ according to the covariance function plot
of Figure 16.5-4a. Visual discrimination can be made in Figure 16.5-5, in which the
correlation parameter differs by 20%. Visual discrimination has been found to be
marginal when the correlation factor differs by less than 10% (19). The first- and
second-order densities of each field are fixed in Figure 16.5-6, and the third-order

528 IMAGE FEATURE EXTRACTION
hA = 0.500, hB = 0.500
sA = 0.167, sB = 0.167
aA = 0.850, aB = 0.850
qA = 0.040, qB = − 0.027
FIGURE 16.5-7. Field comparison of correlated Julesz stochastic fields with identical first-
and second-order densities, but different third-order densities.
pair of similar observation points in both fields. An example of such a pair of fields
is presented in Figure 16.5-7 for a non-Gaussian generating process (19). In this
example, the texture appears identical in both fields, thus supporting the Julesz
conjecture.
Gagalowicz has succeeded in generating a pair of texture fields that disprove the
Julesz conjecture (20). However, the counterexample, shown in Figure 16.5-8, is not
very realistic in appearance. Thus, it seems likely that if a statistically based texture
measure can be developed, it need not utilize statistics greater than second-order.
FIGURE 16.5-8. Gagalowicz counterexample.